Пространственно-типологическая структура и организация населения птиц Тоболо-Иртышской лесостепи и степи Западной Сибири и Северного Казахстана во второй половине лета.

According to the results of bird counts carried out in 138 habitats over 12 years, a hierarchical classification and a structural graph of the similarity of ornithocomplexes in the plain southwestern part of Western Siberia and Northern Kazakhstan have been compiled in the period from 1982 till 2002. The hierarchical classification contains six types of bird populations. The similarity graph is built at the level of types and is represented by three rows (trends). One row consists of bird complexes of residential and recreational areas; the second, of wetlands; and the third, of forest, forest-field, and steppe habitats. The classification taxa characteristics contain information on the three most numerous bird species (leaders in abundance), their share in the community, population density, and the background species wealth. Based on the assessment of the similarity coincidence degree for the of bird communities and environmental factors, a hierarchy of the impact of the main anthropogenic and natural factors, determining the bird population formation, has been established.

A Comparison Study between Autism Spectrum Disorder and Typically Control in Graph Frequency Bands Using Graph and Triadic Interaction Metrics

Many researchers using many different approaches have attempted to find features discriminating between autism spectrum disorder (ASD) and typically control (TC) subjects. In this study, this attempt has been continued by analyzing global metrics of functional graphs and metrics of functional triadic interactions of the brain in the low, middle, and high-frequency bands (LFB, MFB, and HFB) of the structural graph. The graph signal processing (GSP) provided the combinatorial usage of the functional graph of resting-state fMRI and structural graph of DTI. In comparison to TCs, ASDs had significantly higher clustering coefficients in the MFB, higher efficiencies and strengths in the MFB and HFB, and lower small-world propensity in the HFB. These results show over-connectivity, more global integration, and probably decreased local specialization in ASDs compared to TCs. Triadic analysis showed that the numbers of unbalanced triads were significantly lower for ASDs in the MFB. This finding may show the reason for restricted and repetitive behavior in ASDs. Also, in the MFB and HFB, the numbers of balanced triads and the energies of triadic interactions were significantly higher and lower for ASDs, respectively. These findings may reflect the disruption of the optimum balance between functional integration and specialization. All of these results demonstrated that the significant differences between ASDs and TCs existed in the MFB and HFB of the structural graph when analyzing the global metrics of the functional graph and triadic interaction metrics. In conclusion, the results demonstrate the promising perspective of GSP for attaining discriminative features and new knowledge, especially in the case of ASD.

Automated generation of consistent models using qualitative abstractions and exploration strategies

Automatically synthesizing consistent models is a key prerequisite for many testing scenarios in autonomous driving to ensure a designated coverage of critical corner cases. An inconsistent model is irrelevant as a test case (e.g., false positive); thus, each synthetic model needs to simultaneously satisfy various structural and attribute constraints, which includes complex geometric constraints for traffic scenarios. While different logic solvers or dedicated graph solvers have recently been developed, they fail to handle either structural or attribute constraints in a scalable way. In the current paper, we combine a structural graph solver that uses partial models with an SMT-solver and a quadratic solver to automatically derive models which simultaneously fulfill structural and numeric constraints, while key theoretical properties of model generation like completeness or diversity are still ensured. This necessitates a sophisticated bidirectional interaction between different solvers which carry out consistency checks, decision, unit propagation, concretization steps. Additionally, we introduce custom exploration strategies to speed up model generation. We evaluate the scalability and diversity of our approach, as well as the influence of customizations, in the context of four complex case studies.

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

A convex polytope is the convex hull of a finite set of points in the Euclidean space ℝ n . By preserving the adjacency-incidence relation between vertices of a polytope, its structural graph is constructed. A graph is called Hamilton-connected if there exists at least one Hamiltonian path between any of its two vertices. The detour index is defined to be the sum of the lengths of longest distances, i.e., detours between vertices in a graph. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering, whereas the detour index has important applications in chemistry. Checking whether a graph is Hamilton-connected and computing the detour index of an arbitrary graph are both NP-complete problems. In this paper, we study these problems simultaneously for certain families of convex polytopes. We construct two infinite families of Hamilton-connected convex polytopes. Hamilton-connectivity is shown by constructing Hamiltonian paths between any pair of vertices. We then use the Hamilton-connectivity to compute the detour index of these families. A family of non-Hamilton-connected convex polytopes has also been constructed to show that not all convex polytope families are Hamilton-connected.

Isomorphism, canonization, and definability for graphs of bounded rank width

We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k + 4) is a complete isomorphism test for the class of all graphs of rank width at most k. A consequence of our result is the first polynomial time canonization algorithm for graphs of bounded rank width. Our second main result addresses an open problem in descriptive complexity theory: we show that fixed-point logic with counting expresses precisely the polynomial time properties of graphs of bounded rank width.

Wiener index via wirelength of an embedding

Embeddings are often viewed as a high-level representation of systematic methods to simulate an algorithm designed for one kind of parallel machine on a different network structure and/or techniques to distribute data/program variables to achieve optimum use of all available processors. A topological index is a numeric quantity of a molecule that is mathematically derived in an unambiguous way from the structural graph of a molecule. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. Arguably, the best known of these indices is the Wiener index, defined as the sum of all distances between distinct vertices. In this paper, we have obtained the exact wirelength of embedding Cartesian products of complete graphs into a Cartesian product of paths and cycles, and generalized book. In addition to that, we have found the Wiener index of generalized book and the relation between the Wiener index and wirelength of an embedding, which solves (partially) an open problem proposed in Kumar et al. [K. J. Kumar, S. Klavžar, R. S. Rajan, I. Rajasingh and T. M. Rajalaxmi, An asymptotic relation between the wirelength of an embedding and the Wiener index, submitted to the journal].